MCQOPTIONS
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MCQOPTIONS
This section includes 462 Mcqs, each offering curated multiple-choice questions to sharpen your SRMJEEE knowledge and support exam preparation. Choose a topic below to get started.
| 401. |
Number of subsets of a set of order three is |
| A. | 2 |
| B. | 4 |
| C. | 6 |
| D. | 8 |
| Answer» E. | |
| 402. |
The binary relation S = Φ (empty set) on set A = {1, 2,3} is |
| A. | transitive and relexive |
| B. | symmetric and relexive |
| C. | transitive and symmetric |
| D. | neither reflexive nor symmetric |
| Answer» D. neither reflexive nor symmetric | |
| 403. |
Let R be a non-empty relation on a collection of sets defined by ARB if and only if A ∩ B = Ø Then (pick the TRUE statement) |
| A. | R is relexive and transitive |
| B. | R is an equivalence relation |
| C. | R is symmetric and not transitive |
| D. | R is not relexive and not symmetric |
| Answer» D. R is not relexive and not symmetric | |
| 404. |
Which of the following sets are null sets ? |
| A. | { } |
| B. | ø |
| C. | Both (a) and (b) |
| D. | {0} |
| Answer» D. {0} | |
| 405. |
If n(A) = 8, n(A Ç B) = 2, then n(A – B) is equal to: |
| A. | 8 |
| B. | 2 |
| C. | 4 |
| D. | 6 |
| Answer» E. | |
| 406. |
If A = {1, 2, 3} and B = {3, 4}, then (A È B) ´ (A Ç B) is: |
| A. | {3, 3} |
| B. | {(1, 3), (2, 3), (3, 3), (1, 4), (2, 4), (3, 4)} |
| C. | {(1, 3), (2, 3), (3, 3)} |
| D. | {(1, 3), (2, 3), (3, 3), (4, 3)} |
| Answer» E. | |
| 407. |
If A Í B, then A Ç B is equal to: |
| A. | (A – B) Ç (B – A) |
| B. | A – B |
| C. | B – A |
| D. | None of these. |
| Answer» E. | |
| 408. |
A – (B È C) is equal to: |
| A. | (A – B) Ç (A – C) |
| B. | (A – B) È (A – C) |
| C. | (A Ç B) – C |
| D. | None of these. |
| Answer» B. (A – B) È (A – C) | |
| 409. |
In a class of 55 students, the number of students studying different subjects are 23 in mathematics, 24 in physics, 19 in chemistry, 12 in mathematics and physics, 9 in mathematics and chemistry, 7 in physics and chemistry and 4 in all the three subjects. The number of students who have taken exactly one subject is |
| A. | 6 |
| B. | 9 |
| C. | 7 |
| D. | All of these. |
| Answer» E. | |
| 410. |
Two finite sets have m and n elements. Then total number of subsets of the first set is 56 more than that of the total number of subsets of the second. The value of m and n are |
| A. | 7, 6 |
| B. | 6, 3 |
| C. | 5, 1 |
| D. | 8, 7 |
| Answer» C. 5, 1 | |
| 411. |
Sets A and B have 3 and 6 elements each. What can be the minimum number of elements in A È B? |
| A. | 3 |
| B. | 6 |
| C. | 9 |
| D. | None of these |
| Answer» C. 9 | |
| 412. |
In a class 60% passed their Physics examination and 58% passed in Mathematics. Atleast what percentage of students passed both their Physics and Mathematics examination? |
| A. | 18% |
| B. | 17% |
| C. | 16% |
| D. | 2% |
| Answer» B. 17% | |
| 413. |
If A and B both contain same number of elements and are finite sets then |
| A. | n(A È B) = n(A Ç B) |
| B. | n(A ~ B) = n(B ~ A) |
| C. | n(A D B) = n(B) |
| D. | n(A ~ B) = n(A) |
| Answer» C. n(A D B) = n(B) | |
| 414. |
If A and B are two sets such that n (A È B) = 36, n(A Ç B) = 16 and n(A ~ B) = 15, then n(B) is equal to |
| A. | 21 |
| B. | 31 |
| C. | 20 |
| D. | 52 |
| Answer» B. 31 | |
| 415. |
If A is the set of letters needed to spell “MATHEMATICS” and B is the set of letters needed to spell STATISTICS, then |
| A. | A Ì B |
| B. | Y Ì X |
| C. | X = Y |
| D. | None of these |
| Answer» D. None of these | |
| 416. |
If A = {2x : x Î N}, B = {3x : x Î N} and C = {5x : x Î N} then A Ç (B Ç C) is equal to |
| A. | {15, 30, 45,…….} |
| B. | {10, 20, 30,…….} |
| C. | 30, 60, 90,…….} |
| D. | {7, 14, 21,…….} |
| Answer» D. {7, 14, 21,…….} | |
| 417. |
If A = {2, 3, 4, 5, 7}, B = {1, 2, 4, 7, 9} then ((A ~ B) È (B ~ A)) Ç A is equal to |
| A. | {3, 5} |
| B. | {2, 4} |
| C. | {3, 7} |
| D. | {2, 7} |
| Answer» B. {2, 4} | |
| 418. |
A, B, C are three sets such that n(A) = 25, n(B) = 20, n(c) = 27, n(A Ç B) = 5, n(B Ç C) = 7 and A Ç C = f then n(A È B È C) is |
| A. | 60 |
| B. | 65 |
| C. | 67 |
| D. | 72 |
| Answer» B. 65 | |
| 419. |
A, B, C are the sets of letters needed to spell the words STUDENT, PROGRESS and CONGRUENT, respectively. Then n (A È B Ç C) is equal to |
| A. | 8 |
| B. | 9 |
| C. | 10 |
| D. | 11 |
| Answer» C. 10 | |
| 420. |
Let A = {a, b, c} and B = {1, 2}. Consider a relation R defined from set A to set B. Then, R is equal to a subset of |
| A. | A |
| B. | B |
| C. | A×B |
| D. | B×A |
| Answer» D. B×A | |
| 421. |
A relation from P to Q is |
| A. | A universal set of P × Q |
| B. | P × Q |
| C. | An equivalent set of P×Q |
| D. | A subset of P ×Q |
| Answer» E. | |
| 422. |
A relation R from C to R is defined by xR y iff | x | = y. Which of the following is correct? |
| A. | (2 + 3i) R 13 |
| B. | 3 R (– 3) |
| C. | (1 + i) R 2 |
| D. | iR 1 |
| Answer» E. | |
| 423. |
Let R be a relation in N defined by R = {(x, y) : x + 2y = 8}. The range of R is |
| A. | {2, 4, 6} |
| B. | {1, 2, 3} |
| C. | {1, 2, 3, 4, 6} |
| D. | None of these |
| Answer» C. {1, 2, 3, 4, 6} | |
| 424. |
Let A= {1, 2, 3}, B = {1, 3, 5}. If relation R from A to B is given by {(1, 3), (2, 5), (3, 3)} then R – 1 is |
| A. | {(3, 3), (3, 1), (5, 3)} |
| B. | {(1, 3), (2, 5), (3, 3)} |
| C. | {(1, 3), (5, 2)} |
| D. | None of these |
| Answer» E. | |
| 425. |
Let R be a relation in N defined by R = {(1 + x, 1 + x2) : x £ 5, x Î N}. Which of the following is false? |
| A. | R = {(2, 2), (3, 5), (4, 10), (5, 17), (6, 25) |
| B. | Domain of R = {2, 3, 4, 5, 6} |
| C. | Range of R = {2, 5, 10, 17, 26} |
| D. | At least one if false |
| Answer» B. Domain of R = {2, 3, 4, 5, 6} | |
| 426. |
A relation is defined in the set Z of integers as follows (x, y) Î R iff x2 + y2 = 9. Which of the following is false? |
| A. | R = {(0, 3), (0, – 3), (3, 0), (– 3, 0)} |
| B. | Domain of R = {– 3, 0, 3} |
| C. | Range of R = {– 3, 0, 3} |
| D. | At least one if false |
| Answer» B. Domain of R = {– 3, 0, 3} | |
| 427. |
Let A be the set of first ten natural numbers and let R be a relation in A define by (x , y)Î R if and only if x + 2y = 10. Which of the following is false |
| A. | R = {2, 4}, (4, 3), (6, 2), (8, 1) |
| B. | Domain of R = {2, 4, 6, 8} |
| C. | Range of R = {1, 2, 3, 4} |
| D. | At least on is false |
| Answer» E. | |
| 428. |
Let A = {1, 2, 3, 4} and Let R = {(2, 2) (3, 3), (4, 4), (1, 2)} be a relation in A. then R is |
| A. | Reflexive |
| B. | Symmetric |
| C. | Transitive |
| D. | None of these |
| Answer» E. | |
| 429. |
Let X be a family of sets and R be a relation in X defined by ‘A’ is disjoint from B’. The relation R is |
| A. | Reflexive |
| B. | Symmetric |
| C. | Transitive |
| D. | Anti-symmetric |
| Answer» C. Transitive | |
| 430. |
If n/m means that n is a factor m, the relation ‘/’ in z – {0} is |
| A. | Reflexive and symmetric |
| B. | Symmetric ad transitive |
| C. | Reflexive, symmetric and transitive |
| D. | Reflexive, transitive and not symmetric |
| Answer» E. | |
| 431. |
If R is a relation from a set P to set Q, then |
| A. | R Í P × Q |
| B. | R Í Q × P |
| C. | R = P ×Q |
| D. | R = P È Q |
| Answer» B. R Í Q × P | |
| 432. |
If number of elements in sets A and B are m and n respectively, then the number of relations from A to B is |
| A. | 2m +n |
| B. | 2mn |
| C. | m + n |
| D. | mn |
| Answer» C. m + n | |
| 433. |
20 teachers of a school either teach Mathematics or physics. 12 of them teach Mathematics while 4 teach both the subjects. Then, the number of teachers teaching Physics only is |
| A. | 12 |
| B. | 8 |
| C. | 16 |
| D. | None of these |
| Answer» B. 8 | |
| 434. |
Let X and Y be the sets of all positive divisors of 400 and 1000 respectively (including 1 and the number). Then, n (X ÇY) is equal to |
| A. | 4 |
| B. | 6 |
| C. | 8 |
| D. | 12 |
| Answer» E. | |
| 435. |
Two finite sets A and B have m and n elements respectively. If the total number of subsets of A is 112 more than the total number of subsets of B, then the value of m is |
| A. | 7 |
| B. | 9 |
| C. | 10 |
| D. | 12 |
| Answer» B. 9 | |
| 436. |
The relation R defined on the set of natural numbers as {(a, b): a differs from b by 3} is given |
| A. | {(1, 4), (2, 5), (3, 6), ….} |
| B. | { (4, 1), (5, 2), (6, 3), ….} |
| C. | {(4, 1), (5, 2), (6, 3), ….} |
| D. | None of the above |
| Answer» C. {(4, 1), (5, 2), (6, 3), ….} | |
| 437. |
R is a relation on N given by N = {(x, y): 4x + 3y = 20}. Which of the following belongs to R? |
| A. | (– 4, 12) |
| B. | (5, 0) |
| C. | (3, 4) |
| D. | (2, 4) |
| Answer» E. | |
| 438. |
R is a relation from {11, 12, 13} to {8, 10, 12} defined by y = x – 3. The relation R – 1 is |
| A. | {(11, 8), (13, 10)} |
| B. | {(8, 11), (10, 13)} |
| C. | {(8, 11), (9, 12), (10, 13)} |
| D. | None of the above |
| Answer» C. {(8, 11), (9, 12), (10, 13)} | |
| 439. |
If R be relation ‘<‘ from A = {1, 2, 3, 4} to B = {1, 3, 5} ie, (a, b) Î R iff a < b, then RoR– 1 is |
| A. | {(1, 3), (1, 5), (2, 3), (2, 5), (3, 5), (4, 5)} |
| B. | {(3, 1), (5, 1), (3, 2), (5, 2), (5, 3), (5, 4)} |
| C. | {(3, 3), (3, 5), (5, 3), (5, 5)} |
| D. | { (3, 3), (3, 4), (4, 5)} |
| Answer» D. { (3, 3), (3, 4), (4, 5)} | |
| 440. |
Let a relation R in the set R of real numbers be defined as (a, b) Î R if and only if 1 + ab > 0 for all a, bÎR. The relation R is |
| A. | Reflexive and Symmetric |
| B. | Symmetric and Transitive |
| C. | Only transitive |
| D. | An equivalence relation |
| Answer» B. Symmetric and Transitive | |
| 441. |
R is a relation defined in Z by aRb if and only if ab ³ 0, then R is |
| A. | reflexive |
| B. | symmetric |
| C. | transitive |
| D. | equivalence |
| Answer» E. | |
| 442. |
Let X be a family of sets and R be a relation in X, defined by ‘A is disjoint from B’. Then, R is |
| A. | reflexive |
| B. | symmetric |
| C. | anti-symmetric |
| D. | transitive |
| Answer» F. | |
| 443. |
If A = { (1, 2, 3}, then the relation R = {(2, 3)} in A is |
| A. | symmetric and transitive only |
| B. | symmetric only |
| C. | transitive only |
| D. | not transitive |
| Answer» E. | |
| 444. |
If R = {x, y) : x, y Î Z, x2 + y2 £ 4} is a relation in z, then domain of R is |
| A. | {0, 1, 2} |
| B. | {– 2, – 1, 0} |
| C. | {– 2, – 1, 0, 1, 2} |
| D. | None of these |
| Answer» D. None of these | |
| 445. |
The relation R defined on the set A = {1, 2, 3, 4, 5} by R = {(x, y) : | x2 – y2| < 16} is given by |
| A. | {(1, 1), (2, 1), (3, 1), (4, 1), (2, 3)} |
| B. | {(2, 2), (3, 2), (4, 2), (2, 4)} |
| C. | {(3, 3), (4, 3), (5, 4), (3, 4)} |
| D. | None of the above |
| Answer» E. | |
| 446. |
The relation R defined in A = {1, 2, 3} by aRb, if | a2 – b2 | £ 5. Which of the following is false? |
| A. | R = {(1, 1), (2, 2), (3, 3), (2, 1), (1, 2), (2, 3), (3, 2)} |
| B. | R–1 = R |
| C. | Domain of R = {1, 2, 3} |
| D. | Range of R = {5} |
| Answer» E. | |
| 447. |
If A = {1, 2, 4}, B = {2, 4, 5}, C = {2, 5}, then (A – B) ´ (B – C) is |
| A. | {(1, 2), (1, 5), (2, 5)} |
| B. | {(1, 4)} |
| C. | (1, 4) |
| D. | None of these. |
| Answer» C. (1, 4) | |
| 448. |
If A = {2, 3} and B = {x | x Î N and x < 3}, then A ´ B is |
| A. | {(2, 1), (2, 2), (3, 1), (3, 2)} |
| B. | {(1, 2), (1, 3), (2, 2), (2, 3)} |
| C. | {(1, 2), (2, 2), (3, 3), (3, 2) |
| D. | None of these. |
| Answer» B. {(1, 2), (1, 3), (2, 2), (2, 3)} | |
| 449. |
If A = {a, b, c}, B = }c, d, e}, C = {a, d, f}, then A ´ (B È C) is |
| A. | {(a, d), (a, e), (a, c)} |
| B. | {(a, d), (b, d), (c, d)} |
| C. | {(d, a), (d, b), (d, c)} |
| D. | None of these. |
| Answer» E. | |
| 450. |
If A = {1, 2, 3}, B = {4, 5, 6} and C = {1, 2}, then (A – B) ´ (A Ç C) is |
| A. | {(1, 3), (1, 5)} |
| B. | {(2, 1), (2, 2), (2, 3)} |
| C. | {(1, 2), (1, 3), (1, 5)} |
| D. | None of these |
| Answer» E. | |